To make both expressions {(x^2 + y^2 – 1), (x^2 – y^2 – 1)} square

 
 
x^2 \; + \; y^2 \; - \; 1
x^2 \; - \; y^2 \; - \; 1

 
Here are the first few solutions
 

9^2 \; + \; 8^2 \; - \; 1 \; = \; 12^2
9^2 \; - \; 8^2 \; - \; 1 \; = \; 4^2

129^2 \; + \; 64^2 \; - \; 1 \; = \; 144^2
129^2 \; - \; 64^2 \; - \; 1 \; = \; 112^2

649^2 \; + \; 216^2 \; - \; 1 \; = \; 684^2
649^2 \; - \; 216^2 \; - \; 1 \; = \; 612^2

2049^2 \; + \; 512^2 \; - \; 1 \; = \; 2112^2
2049^2 \; - \; 512^2 \; - \; 1 \; = \; 1984^2

5001^2 \; + \; 1000^2 \; - \; 1 \; = \; 5100^2
5001^2 \; - \; 1000^2 \; - \; 1 \; = \; 4900^2

10369^2 \; + \; 1728^2 \; - \; 1 \; = \; 10512^2
10369^2 \; - \; 1728^2 \; - \; 1 \; = \; 10224^2

19209^2 \; + \; 2744^2 \; - \; 1 \; = \; 19404^2
19209^2 \; - \; 2744^2 \; - \; 1 \; = \; 19012^2

 

Determine the recursion formula

 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
This entry was posted in Number Puzzles and tagged . Bookmark the permalink.

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